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1 13. (a) Prove: If A is invertible, then det(A-1) = A %3D det(A) (b) Prove: If A is invertible, then adj(A) is invertible and [adj(A-!)] = Za4- = adj(A). %3D det(A-) (Hint: you may use part (a) to prove part (6) of this proof)

1 13. (a) Prove: If A is invertible, then det(A-1) = A %3D det(A) (b) Prove: If A is invertible, then adj(A) is invertible and [adj(A-!)] = Za4- = adj(A). %3D det(A-) (Hint: you may use part (a) to prove part (6) of this proof)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1 13. (a) Prove: If A is invertible, then det(A-1) = A (b) Prove: If A is invertible, then adj(A) is invertible and [adj(A-1)]-1 = A-1 = adj(A). det(A) det (A-) (Hint: you may use part (a) to prove part (b) of this proof) c梦0 P Type here to search hp Design Using Autodesk Revit 2020 1444444 Cintel TORIALAI STANINZA
Transcribed Image Text:1 13. (a) Prove: If A is invertible, then det(A-1) = A (b) Prove: If A is invertible, then adj(A) is invertible and [adj(A-1)]-1 = A-1 = adj(A). det(A) det (A-) (Hint: you may use part (a) to prove part (b) of this proof) c梦0 P Type here to search hp Design Using Autodesk Revit 2020 1444444 Cintel TORIALAI STANINZA
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